Hi,
I'm really sorry you had to go through that. I had a similar experience (before I started getting migraines, actually) with a doctor refusing to do anything else to help me with sleep problems unless I took a particular anxiety drug for at least a month first, and it really sucked. It was the same situation - she gave me zero alternative options and just kept pushing the one drug. Sometimes I wonder if I would have started getting migraines or not if my sleep problems had been addressed effectively back then... Anyway you're not alone and I really hope you can find a new doctor soon.
I've linked to a video below that was really eye-opening for me regarding why doctors sometimes push specific medicines so much. Unfortunately money talks, and pharmaceutical companies spend a lot on getting doctors to prescribe their products. It's important to be aware of, and I would be suspicious of any doctor that's really pushing one medicine at you instead of giving you multiple options and openly and honestly discussing the side effects of each. (The video is done by comedian John Oliver - apologies if his humor isn't to everyone's taste but he explains the issue really, really well): https://www.youtube.com/watch?v=YQZ2UeOTO3I
Also, your doctor is totally wrong about food not playing a role in your migraines. You know your body better than anyone, so if you feel like foods/digestive issues are causing your migraines, you're probably right. I don't know if you've tried a migraine elimination diet yet, but if you haven't that would be a good place to start (http://www.fammed.wisc.edu/sites/default/files/webfm-uploads/documents/outreach/im/handout_ha_elim_diet_patient.pdf). Just keep in mind that food triggers can be really different for different people and you may have some that aren't on most of the 'food trigger' lists - for example, sugar can be a trigger for me and a couple other people I know. And I totally agree with the person above about finding a different specialist to work on digestive issues with.
Also, I don't know if you have access to a naturopathic doctor, but a big part of their philosophy is how everything in the body is connected, whereas in conventional medicine they usually just want to treat one part of the body or one set of symptoms at a time, and treat every health issue as separate instead of connected. If you can find a naturopathic (or ayurvedic) doctor they might be able to provide some insight into how those things are connected that a regular doctor might not.
Good luck and I hope you can find a better doctor that can help you!